Rodney is trying out one of Santa's new games that consists of three pieces that blow apart if the wrong key is inserted into the door. The elf picks the wrong key and the board explodes. One piece of mass 2 kg goes off at an angle of 60° from the horizon at 10 m/s. A second piece of mass 1.2 kg travels at an angle of 180° and is moving at 15 m/s.

a) find the momentum of the third piece.

b) find the velocity of the third piece if it's mass is 3 kg.

Answers

Answer 1

Answer:

The third piece moves at 6.36 m/s at an angle of 65° below the horizon

Explanation:

Linear Momentum

It's a physical magnitude that measures the product of the velocity by the mass of a moving object. In a system where no external forces are acting, the total momentum remains unchanged regardless of the interactions between the objects in the system.

If the velocity of an object of mass m is [tex]\vec v[/tex], the linear momentum is computed by

[tex]\displaystyle \vec{P}=m.\vec{v}[/tex]

a)

The momentum of the board before the explosion is

[tex]\displaystyle \vec{P}_{t1}=m_t\ \vec{v}_o[/tex]

Since the board was initially at rest

[tex]\displaystyle \vec{P}_{t1}=<0,0>[/tex]

After the explosion, 3 pieces are propelled in different directions and velocities, and the total momentum is

[tex]\displaystyle \vec{P}_{t2}=m_1\ \vec{v}_1\ +\ m_2\ \vec{v}_2+m_3\ \vec{v}_3[/tex]

The first piece of 2 kg moves at 10 m/s in a 60° direction

[tex]\displaystyle \vec{v}_1=(10\ m/s,60^o)[/tex]

We find the components of that velocity

[tex]\displaystyle \vec{v}_1=<10\ cos60^o,10\ sin60^o>[/tex]

[tex]\displaystyle \vec{v}_1=<5,5\sqrt{3}>m/s[/tex]

The second piece of 1.2 kg goes at 15 m/s in a 180° direction

[tex]\displaystyle \vec{v}_2=(15,180^o)[/tex]

Its components are computed

[tex]\displaystyle \vec{v}_2=(15\ cos180^o,15\ sin180^o)[/tex]

[tex]\displaystyle \vec{v}_2=(-15,0)\ m/s[/tex]

The total momentum becomes

[tex]\displaystyle P_{t2}=2<5,5\sqrt{3}>+1.2<-15,0>+m_3\ \vec{v}_3[/tex]

Operating

[tex]\displaystyle P_{t2}=<10,10\sqrt{3}>+<-18,0>+m_3\ \vec{v}_3[/tex]

Knowing the total momentum equals the initial momentum

[tex]\displaystyle P_{t2}=<-8,10\sqrt{3}>+m_3\ \vec{v}_3=0[/tex]

Rearranging

[tex]\displaystyle m_3\ \vec{v}_3=<8,-10\sqrt{3}>[/tex]

Calculating

[tex]\displaystyle m_3\ \vec{v}_3=<8,-17.32>[/tex]

This is the momentum of the third piece

b)

From the above equation, we solve for [tex]\vec v_3[/tex]:

[tex]\displaystyle \vec{v}_3=\frac{1}{3}<8,-17.32>[/tex]

[tex]\displaystyle \vec{v}_3=<2.67,-5.77>m/s[/tex]

The magnitude of the velocity is

[tex]\displaystyle \vec{v}_3|=\sqrt{2.67^2+(-5.77)^2}=6.36[/tex]

And the angle is

[tex]\displaystyle tan\theta =\frac{-5.77}{2.67}=-2.161[/tex]

[tex]\displaystyle \theta =-65.17^o[/tex]

The third piece moves at 6.36 m/s at an angle of 65° below the horizon


Related Questions

A girl is riding her bike at as speed of 12 m/s. She weighs 55 kg and her bike weighs 22kg. What is the kinetic energy of the girl and her bike?

Answers

Answer:

Kinetic energy of the girl and her bike is 5.544 kJ

Explanation:

Given that a girl is riding bike at speed of 12m/s

Also, mass of Girl is 55kg and mass of bike is 22kg

Let, Total mass of girl and bike be M=22+55=77kg

Now, Kinetic energy is given by K=[tex]\frac{1}{2} Mv^{2}[/tex]

Hence, Kinetic energy of the girl and her bike will be

K=[tex]\frac{1}{2} Mv^{2}[/tex]

K=[tex]\frac{1}{2} (77)(12)^{2}[/tex]

K=5544J

Thus, Kinetic energy of the girl and her bike is 5.544 kJ

Find the resistance of an iPhone battery if it is a 5.0V charger at 2.1 A

Answers

Answer:

2.38Ω

Explanation:

We are given;

Voltage as 5.0 V Current as 2.1 A

We are required to calculate the resistance of the iPhone battery;

According to Ohm's law, the current through a conductor is directly proportional to the potential difference at constant temperature and pressure.That is; V = IR Rearranging the formula;

R = V/I

Therefore;

R = 5.0 V ÷ 2.1 A

  = 2.38 Ω

Thus, the resistance of the iPhone battery is 2.38Ω

For the resistance of an iPhone battery connected to a 5.0V charger at 2.1A, you can use Ohm's Law to calculate the resistance as approximately 2.38 ohms.

The resistance of a battery is determined using Ohm's Law, where resistance (R) equals voltage (V) divided by current (I). In this case, a 5.0V charger at 2.1A results in a resistance of 2.38 ohms.

Calculate the volume of 1280 kilograms of aluminium if the density of aluminium is 2700 kg/m³. Give your answer to 2 decimal places.

Answers

Answer:

volume = 0.47 [tex]m^{3}[/tex].

Explanation:

Density:

[tex]d = \frac{m}{v}[/tex]

We have that d = 2700 kg/[tex]m^{3}[/tex] and that we have 1280 kg of Al.

[tex]2700 = \frac{1280}{V}[/tex]

V = 0.47 [tex]m^{3}[/tex]

Answer:

The correct answer is 0.47 m³

Explanation:

The formula for density (d) is

Mass (m) ÷ volume (v)

Hence

d = m ÷ v

The density of aluminium (as provided in the question) is 2700  kg/m³ and the mass of aluminium is 1280 kg, the volume is however unknown.

Thus, from the formula earlier

2700 = 1280 ÷ v

v = 1280 ÷ 2700

v = 0.47 m³

The volume of aluminium when the density is 2700  kg/m³ and the mass is 1280 kg is 0.47 m³

A boy standing on the top of a cliff projects an object upwards with a velocity of 60m/s.
After 10s he releases anothe object from the cliff so that the 2 obects meet at a specific point. Find the distance from the top of the cliff to the point these objects meet with the correct  explanation .
 (Ans. 31.25m)
please i need help in this​

Answers

Explanation:

For projectile motion, use constant acceleration equation:

Δx = v₀ t + ½ at²

where Δx is the displacement,

v₀ is the initial velocity,

a is the acceleration,

and t is time.

For the first object:

Δx = 60 t + ½ (-10) t²

Δx = 60 t − 5 t²

For the second object:

Δx = 0 (t−10) + ½ (-10) (t−10)²

Δx = -5 (t−10)²

When they meet, they have the same displacement, so:

60 t − 5 t² = -5 (t−10)²

60 t − 5 t² = -5 (t² − 20t + 100)

60 t − 5 t² = -5 t² + 100 t − 500

60 t = 100 t − 500

40 t = 500

t = 12.5

Plug into either of the original equations to find the displacement.

Δx = -5 (t−10)²

Δx = -5 (12.5−10)²

Δx = -31.25

The distance from the top of the cliff to the point where the objects meet is 31.25 meters.

How much heat does it take to raise the temperature of 0.10kg of gold by 25°C

Answers

Answer:

322.5 joules

Explanation:

Data given;

Mass of Gold is 0.10 kg Change in temperature as 25°C

We are supposed to determine the amount of heat required.

We know that quantity of heat is given by the product of mass of a substance by its specific heat and by the change in temperature.That is, Q = mcΔT

In this case, specific heat, c of gold is 0.129 J/g/°C

Mass of gold in grams is 100 g

Therefore;

Q = 100 g × 0.129 J/g/°C × 25°C

   = 322.5 joules

Thus, the amount of heat required is 322.5 Joules

The
of an object consists of its speed and direction.
a. Average speed
b. Instantaneous speed
c. Velocity
d. Displacement

Answers

Answer:

c. Velocity

Explanation:

Velocity is a measure of change of position of the body with time. Change of position means the distance traveled by the object in a given interval of time but in a particular direction.

We know that speed is given as the distance traveled over a given time interval without taking into account the direction of motion. So, the magnitude of velocity is same as its speed. Velocity, being a vector quantity, has both magnitude and direction.

Therefore, the velocity of an object consists of its speed and direction.

Suppose you throw a rock off a cliff on Earth with an initial horizontal velocity of 3 m/s. Assuming minimal drag and no wind, the horizontal velocity of the rock A. increases as it falls. B. decreases as it falls. C. is 0 m/s just before it lands. D. remains constant throughout the fall.

Answers

The horizontal velocity D. remains constant throughout the fall.

Explanation:

The motion of the rock off the cliff is a projectile motion, which consists of two independent motions:

A horizontal uniform motion. Since there are no forces acting along the horizontal direction (we consider the air drag to be negligible), the acceleration along this direction is zero, so the horizontal component of the velocity is constantAn accelerated motion with constant acceleration. There is one force acting along the vertical direction, the force of gravity, which is constant so the rock experiences a constant acceleration (downward) of magnitude [tex]g=9.8 m/s^2[/tex] (acceleration of gravity). This means that the vertical component of the velocity keeps changing.

Here in this problem, we are only interested in the horizontal velocity. We said that the horizontal acceleration of the rock is zero: therefore, the horizontal velocity of the rock remains constant during the fall. (if the air drag was not negligible, then it would affect the horizontal velocity, which would decrease as the rock falls).

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Which phase of the moon is represented by position 4?

A. New moon

B. First quarter

C. Waxing gibbous

D. Waning gibbous

Answers

Answer:

Its C waxing gibbous

Explanation:

if an offspring inherits chromosome 1a,the protein for what color flower can be produce?

Answers

Answer:

Your mother can tell you that answer

Explanation:

2 1100 kg cars drive east; the first moving at 30 m/s the 2nd at 15 m/s what is the magnitude of the total momentum of the system​

Answers

Final answer:

The magnitude of the total momentum of the system of two cars, each with a mass of 1100 kg and moving east at 30 m/s and 15 m/s respectively, is 49500 kg·m/s east.

Explanation:

To calculate the total momentum of the system consisting of two cars driving east, you need to use the formula for momentum, which is the product of mass and velocity (p = mv). The momentum of each car is calculated separately and then added together since they are moving in the same direction (east).

For the first car with a mass of 1100 kg moving at 30 m/s, its momentum is:

p1 = m1 * v1 = 1100 kg * 30 m/s = 33000 kg·m/s.

For the second car with the same mass of 1100 kg but moving at 15 m/s, its momentum is:

p2 = m2 * v2 = 1100 kg * 15 m/s = 16500 kg·m/s.

The total momentum of the system is the sum of the momenta of both cars:

total p = p1 + p2 = 33000 kg·m/s + 16500 kg·m/s = 49500 kg·m/s.

Therefore, the magnitude of the total momentum of the system is 49500 kg·m/s to the east.

A girl runs 20.9 m/s East for 13.7s. How far does she go?

Answers

20.9m = 1s

286.33m = 13.7s

To answer this you would multiply both sides by the amount of seconds she ran. The answer however is that she ran as far as 286.33m.

Answer: 286.33

Explanation:

multiplay them

What do human beings get from forest?​

Answers

Answer:

Oxygen. When trees "breathe" they release oxygen and take in the carbon dioxide. On the other hand, when humans breathe we take in that oxygen and release carbon dioxide. In this way, we have a relationship that is mutually beneficial.

We get trees, which produces oxygen. Which is the air we need to breathe.
Forests provide greenery, which is essential to a healthy environment on earth.
Forests provide habitat for all animals in ecosystems and biomes.
Forests are used to create products such as paper and other materials.
Forests are also apart of nature, which as humans we develop connection to nature by spending time outside and caring for the earth.
Please vote my answer brainliest, thanks!

Is the relationship between velocity and centripetal force a direct, linear or nonlinear square relationship?

Answers

Answer:

non linear square relationship

Explanation:

formula for centripetal force is given as

a = mv^2/r

here a ic centripetal acceleration , m is mass of body moving in circle of radius r and v is velocity of body . If m ,and r are constant we have

a = constant × v^2

a α v^2

hence non linear square relationship

The relationship between velocity and centripetal force is a nonlinear square relationship.

The centripetal force is given by;

F = mv^2/r

The centripetal force is the force required to keep an object moving in a circular path.

If we take the relationship between the centripetal force and velocity as we can see in the equation above, we realize that it is a nonlinear square relationship. Therefore, the relationship between velocity and centripetal force is a nonlinear square relationship.

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HELP ASAP! A certain wave has a frequency of 200 Hz and a wavelength of 2 meters. Calculate the wave speed. SHOW WORK! Question 13 options:

Answers

Answer:

400 m/s

Explanation:

From the question;

The frequency of the wave is 200 Hz Wavelength of the wave is 2 meters

We are required to calculate the speed of the wave;

We need to know that the speed of the wave is calculated by multiplying frequency by the wavelength of the wave.That is, speed = wavelength × frequency In this case;

Speed of the wave = 200 Hz × 2 m

                               = 400 m/s

Thus, the speed of the wave is 400 m/s

SECTION B
THEORY QUESTIONS
(1a) Define the following
(a) Work:​

Answers

Work is the amount of energy transferred

Explanation:

In physics, work is a measure of the energy transfer occurring in a process. Typically, we talk about work when energy is converted from one form into another.

For instance, work is done when a force is applied on an object. The work done on the object is given by:

[tex]W=Fd cos \theta[/tex]

where

where

F is the magnitude of the force

d is the displacement

[tex]\theta[/tex] is the angle between the direction of the force and of the displacement

We notice the following:

No work is done when the force is perpendicular to the displacement ([tex]cos 90^{\circ}=0[/tex])The work is maximum when the force is parallel to the displacement

Whenever work is done, there is also an energy transfer taking place. For instance, in the previous example, when the force is applied to the object, the object will accelerate (assume there is no friction), and will gain kinetic energy: therefore, there is a transfer of energy to the object.

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A snowball accelerates at
23.4 m/s? when a 2.87 N
force is exerted on it. What is
the mass of the snowball?
(Unit = kg)

Answers

Answer:

0. 1226495726kg

Explanation:

Force is the product of mass and acceleration.

Mathematically,

Force(F) = mass (m)×acceleration(a)

Substituting the values into the equation

2. 87=m×23. 4

2. 87=m (23. 4)

2. 87/23. 4=m (23. 4)/23. 4

2. 87/23. 4=m

0. 1226495726=m

Answer:

Answer:

0. 1226495726kg

Explanation:

Force is the product of mass and acceleration.

Mathematically,

Force(F) = mass (m)×acceleration(a)

Substituting the values into the equation

2. 87=m×23. 4

2. 87=m (23. 4)

2. 87/23. 4=m (23. 4)/23. 4

2. 87/23. 4=m

0. 1226495726=m

Explanation:

A light wave traveling through an unknown medium strikes the boundary with
water at a 45° angle and then refracts toward the boundary. What could the

Answers

Final answer:

If light refracts toward the normal when passing from water to an unknown medium, it indicates that the unknown medium has a higher index of refraction than water.

Explanation:

When light waves travel through water and encounter a boundary with another medium at a non-normal angle, they undergo refraction. If the medium has an index of refraction higher than that of water, the light waves slow down, bending toward the normal due to the change in speed. According to Snell's law, the path of light is dependent on the indices of refraction of the two media and the angle of incidence. In this case, if the angle of refraction is closer to the normal compared to the angle of incidence, it indicates that the unknown medium has a higher index of refraction than water.


What station broadcasts waves with more energy? (WIL-92.3 OR KSHE-94.7)

Answers

Answer:

KSHE [tex]94.7[/tex]

Explanation:

Given stations WIL [tex]92.3[/tex] and KSHE [tex]94.7[/tex]

The station number represents the frequency that waves of radio emit. They are measured in megahertz (MHZ).

Using the formula  

[tex]E=h\nu[/tex]

Where [tex]E[/tex] is energy.  

[tex]h[/tex] is Planck's constant.

[tex]\nu[/tex] is frequency.

We can see energy is directly related to frequency. A higher frequency will give higher energy.  

As channel KSHE [tex]94.7[/tex] has more frequency than channel WIL [tex]92.3[/tex].  

So, channel KSHE [tex]94.7[/tex] will have more energy.

Susan goes out to exercise. She runs for one hour at a constant speed and velocity. What is the overall net force acting on
Susan?

Answers

Answer:

Overall net force is zero.

Explanation:

Given:

Susan exercise for 1 hour at constant velocity and constant speed.

So, there is no change in the velocity for 1 hour.

We know that, acceleration is the quantity that measures the change in velocity over a given time interval. If there is no change in velocity or if velocity remains constant for a given time interval, then the acceleration of the body is zero.

Now, from Newton's second law, we know that, the net force acting on a body is directly proportional to its acceleration. Therefore, for a body to experience zero acceleration means that the body will have zero net force.

Susan here exercises at constant velocity and so, her net acceleration is zero. Therefore, the overall net force acting on her will also be zero as net force is directly proportional to the acceleration.

Final answer:

In an ideal scenario ignoring external factors, the overall net force acting on Susan while she runs at a constant speed and velocity is zero, as per Newton's first law of motion.

Explanation:

The question is concerned with a scenario where Susan is running at a constant speed and velocity, implying that she is not accelerating. According to Newton's first law of motion, also known as the law of inertia, an object in motion at a constant velocity will remain in motion at that velocity unless acted upon by a net external force. Since Susan is running at a constant speed and velocity, this means there is no net external force acting on her because all forces are balanced.

Based on Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (Fnet = ma), and given that Susan is not accelerating (acceleration is zero), the net force acting on her is also zero. This assumes ideal conditions where external factors like air resistance and friction are negligible or perfectly balanced by Susan’s forward force.

jessica stretches her arms out to 0.6m from the center of her body while holding a 2 kg mass in each hand She then spins around on an ice rink at 1.1m/s.
If she pulls her arms in to .15 m, what is her linear speed if the angular momentum remains constant?

Answers

Answer:

4.4 m/s

Explanation:

Angular momentum is:

L = Iω

For a point mass, this can also be written as:

L = mvr

Angular momentum is conserved, so:

L₁ = L₂

m₁ v₁ r₁ = m₂ v₂ r₂

(2 kg) (1.1 m/s) (0.6 m) = (2 kg) v (0.15 m)

v = 4.4 m/s

Help me Plz
can you solve the upper photo for me​

Answers

1) The acceleration of the plane is 1.89 times the acceleration of gravity

2) The force acting on the airplane is [tex]2.22\cdot 10^5 N[/tex]

Explanation:

1)

The acceleration of the plane is given by

[tex]a=\frac{v-u}{t}[/tex]

where

v is the final velocity of the plane

u is the initial velocity

t is the time elapsed

For the airplane in this problem, we have:

[tex]u=0[/tex] (it starts from rest)

[tex]v=200 km/h \cdot \frac{1000 m/km}{3600 s/h}=55.6 m/s[/tex] is the final velocity

[tex]t=3 s[/tex] is the time

Substituting, we find

[tex]a=\frac{55.6-0}{3}=18.5 m/s^2[/tex]

The acceleration of gravity is

[tex]g=9.8 m/s^2[/tex]

So, the acceleration of the plane relative to [tex]g[/tex] is

[tex]\frac{a}{g}=\frac{18.5}{9.8}=1.89[/tex]

2)

The average force exerted on the plane is given by Newton's second law:

[tex]F=ma[/tex]

where

F is the force

m is the mass of the airplane

a is the acceleration

In this problem, we have

[tex]m=12000 kg[/tex] is the mass of the plane

[tex]a=18.5 m/s^2[/tex] is the acceleration

Substituting, we find:

[tex]F=(12000)(18.5)=2.22\cdot 10^5 N[/tex]

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What is DC in electricity mean?

Answers

Answer:

Direct Current

Explanation:

The electricity only flows in one direction.

what object did you choose to put on the skateboard ​

Answers

The object that I did choose to put on the skateboard ​ is a sticky ball.

Is skateboarding a form of a good exercise?

A sports scientists is said to have confirmed that skateboarding is seen to be a very goof and complete workout.

Note that  It not only functions along the cardiovascular system and it also helps to create muscular strength. The core of a skateboarder is seen as very crucial role.

The object that I did choose to put on the skateboard ​ is a sticky ball and it is one where i can measure the velocity as well as the speed taken.

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Skateboard falls with force of weight pulling downwards with 53 Newton’s accelerating at a rate of 9.81m/s what’s the mass of the skateboard

Answers

Point of correction, acceleration is 9.81 m/s2

Answer:

5.4 Kg

Explanation:

We know that F=ma and making m the subject of the formula then

[tex]m=\frac {F}{a}[/tex] where m is the mass of the skateboard, F is the pulling force and a is the acceleration of the body

Substituting 53 N for F and 9.81 m/s2 for a then

[tex]m=\frac {53 N}{9.81 m/s2}=5.40265 Kg\approx 5.4 Kg[/tex]

What is the kinetic energy of an object that has a mass of 50 kg in a velocity of 18 m/s

Answers

Answer:

8100 J

Explanation:

KE = ½ mv²

KE = ½ (50 kg) (18 m/s)²

KE = 8100 J

A rubbit gets down from a rump which its /\x=0.85m in 0.5s, The rubbit's mass is 2kg, what is the net Force?

Answers

Answer: 13.6 N

Explanation:

The equation of motion for the rabbit is:

[tex]\Delta x=V_{ox}t+\frac{1}{2}a_{x}t^{2}[/tex] (1)

Where:

[tex]\Delta x=0.85 m[/tex] is the distance traveled by the rabbit

[tex]V_{ox}=0 m/s[/tex] is the rabbit's initial velocity, assuming it started from rest

[tex]t=0.5 s[/tex] is the time

[tex]a_{x}[/tex] is the acceleration

Isolating [tex]a_{x}[/tex]:

[tex]a_{x}=\frac{2 \Delta x}{t^{2}}[/tex] (2)

[tex]a_{x}=\frac{2 (0.85 m)}{(0.5)^{2}}[/tex] (3)

[tex]a_{x}=6.8 m/s^{2}[/tex] (4)

On the other hand, the force [tex]F_{x}[/tex] is given by:

[tex]F_{x}=m.a_{x}[/tex] (5)

Where [tex]m=2 kg[/tex] is the mass of the rabbit

Substituting (4) in (5):

[tex]F_{x}=(2 kg)(6.8 m/s^{2})[/tex] (6)

Finally:

[tex]F_{x}=13.6 N[/tex]

When light is reflected, the "outgoing" ray is also called the _____ ray.
A. incident
B. reflected
C. bouncing
D. electromagnetic

Answers

Answer:

When light is reflected, the "outgoing" ray is also called the reflected ray.

Explanation:

when an light ray is incident on a boundary of two mediums it an reflect or refract.

reflected ray is the part of the ray that gets back with same mediu that it was coming from. angle of reflection and incident are equal . angle of reflection and incident are the angle made by the reflected and incident ray with the normal.

total internal reflection occurs when the incident angle is greater than the critical angle of pair of given medium and when light travels from denser to rarer medium . in total internal reflection ray gets reflected with no loss at all.

in refracted ray the the light ray passes to the other medium angle of incidence and refraction are not same.

PLEASE HELP QUICKLY!!
Define and compare the relationship between the following principles. Provide a supporting example for each
comparison

• Original Horizontality

• Original Lateral Extension

•Cross-Cutting Relationships

•Inclusion

•Uniformities

Answers

Answer:

These 5 principles can be better understood from the past events as well as from formation of the sedimentary rocks

Explanation:

Principle of original horizontal- the sedimentary rocks are found to be horizontal during the initial deposits phase. If  tilted this is due to the subsequent geological event.

Principle of original lateral continuity- The sedimentary beds are originally laterally continuous into their environment of deposition. Faulting in the severe folding and also erosion may leads to the separation of the originally lateral continuous beds which in later becomes separate units.

Principle of cross cutting- The younger features can get cuts across the older features. That's why faults,  erosion, volcanoes etc can be seen. The above mentioned are younger than those materials that is faulted intruded, or eroded.

Principle of inclusion- Inclusion itself means (a rock fragment another rock fragment) they must be older than the materials in.

Principle of uniformity-  Those are the physical process that are been seen today, were also worked in the same way in the geologic past, thus modern methods helps us to understand the ancient events.

So I answered this question and I got it wrong. The correct answer is in red. Can someone explain me why the correct answer is 140s/the temperature starts to rise? I don't understand it. ​

Answers

i) The lowest temperature recorded is [tex]12^{\circ}C[/tex]

ii) All the liquid has evaporated after 140 seconds

Explanation:

i)

In this part of the problem, we have to find the lowest temperature recorded as the liquid evaporates.

In order to do that, we have to look at the graph, where we have:

- The time (in seconds) represented on the x-axis

- The temperature (in Celsius degrees) represented on the y-axis

The lowest temperature recorded corresponds to the minimum value of the variable on the y-axis. By looking at the graph, we see that the temperature starts from [tex]20^{\circ}[/tex] at time [tex]t=0[/tex], then it reaches a minimum of approximately [tex]12^{\circ}C[/tex] at about [tex]t=140 s[/tex], then it increases again. Therefore, the lowest temperature recorded is [tex]12^{\circ}C[/tex].

ii)

In this part, we have to determine how long it takes for all the liquid to evaporate.

The process of evaporation of a liquid takes place when the molecules located on the surface of the liquid, which have more kinetic energy than the other molecules, "escape" the liquid. When these molecules escape the liquid, they remove heat from the liquid (because they carry away energy): therefore, the temperature (which is a measure of the kinetic energy) at the surface of the liquid decreases. This effect is known as cooling effect of evaporation.

When this decrease in temperature stops, it means that the liquid has completely evaporated. From the graph, we see that this occurs when the time is approximately about 140 seconds.

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Explain the arguments for and against the theory that animals have the capacity for language, like humans.
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Final answer:

The arguments for and against the theory that animals have the capacity for language, like humans, revolve around communication abilities and linguistic complexity. Some argue that animals can communicate using complex systems of signs, sounds, and gestures, while others claim that their communication lacks the complexity and structure of human language.

Explanation:

There are arguments both for and against the theory that animals have the capacity for language, like humans. Some argue that animals do have the capacity for language based on their ability to communicate with each other and with humans using complex systems of signs, sounds, and gestures. For example, dolphins use a system of clicks and whistles to communicate with each other. Some primates have been taught sign language and can use it to communicate with humans.

On the other hand, some argue that animals do not have the same capacity for language as humans. They point out that while animals can communicate, their communication lacks the complexity and structure found in human language. Animal communication is often limited to simple signals or gestures, rather than the complex syntax and grammar of human language.

Additionally, animals do not exhibit the same level of linguistic creativity and symbolic thought as humans. For example, humans can use language to discuss abstract concepts, tell stories, and express emotions, whereas animals typically use communication for more practical purposes such as signaling danger or finding food.

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